### Abstract

Original language | English |
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Title of host publication | Mathematics of Surfaces XII |

Subtitle of host publication | Mathematics of Surfaces 2007 |

Editors | R. Martin, M. Sabin, J. Winkler |

Publisher | Springer |

Pages | 391-411 |

ISBN (Electronic) | 978-3-540-73843-5 |

ISBN (Print) | 978-3-540-73842-8 |

DOIs | |

Publication status | Published - 4 Sep 2007 |

Event | 2007 IMA International Conference on Mathematics of Surfaces: Mathematics of Surfaces 2007 - Sheffield, United Kingdom Duration: 4 Sep 2007 → 6 Sep 2007 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 4647 |

### Conference

Conference | 2007 IMA International Conference on Mathematics of Surfaces |
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Country | United Kingdom |

City | Sheffield |

Period | 4/09/07 → 6/09/07 |

### Fingerprint

### Cite this

*Mathematics of Surfaces XII : Mathematics of Surfaces 2007*(pp. 391-411). (Lecture Notes in Computer Science; Vol. 4647). Springer. https://doi.org/10.1007/978-3-540-73843-5_24

**Bounded Curvature Without Eigenanalysis.** / Sabin, Malcolm A. ; Cashman, Thomas J. ; Augsdörfer, Ursula; Dodgson, Neil A. .

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

*Mathematics of Surfaces XII : Mathematics of Surfaces 2007.*Lecture Notes in Computer Science, vol. 4647, Springer, pp. 391-411, 2007 IMA International Conference on Mathematics of Surfaces, Sheffield, United Kingdom, 4/09/07. https://doi.org/10.1007/978-3-540-73843-5_24

}

TY - GEN

T1 - Bounded Curvature Without Eigenanalysis

AU - Sabin, Malcolm A.

AU - Cashman, Thomas J.

AU - Augsdörfer, Ursula

AU - Dodgson, Neil A.

PY - 2007/9/4

Y1 - 2007/9/4

N2 - It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This paper provides an alternative insight, based on the use of second divided differences, and applies it to three familiar schemes. A single concept is shown to work in three different contexts. In each case a bounded curvature variant results, with a very simple and elegant implementation.

AB - It has long been known how to achieve bounded curvature at extraordinary points of a subdivision scheme by using eigenanalysis and then adjusting the mask of each extraordinary point. This paper provides an alternative insight, based on the use of second divided differences, and applies it to three familiar schemes. A single concept is shown to work in three different contexts. In each case a bounded curvature variant results, with a very simple and elegant implementation.

U2 - 10.1007/978-3-540-73843-5_24

DO - 10.1007/978-3-540-73843-5_24

M3 - Conference contribution

SN - 978-3-540-73842-8

T3 - Lecture Notes in Computer Science

SP - 391

EP - 411

BT - Mathematics of Surfaces XII

A2 - Martin, R.

A2 - Sabin, M.

A2 - Winkler, J.

PB - Springer

ER -